Find the exact value of each expression. sin⁻¹ √2/2

Question

Accepted Answer

Hello everybody. I hope we're doing tonight today. Today we're going to be looking at this question that states for the following trigonometric expression evaluate and give the answer as an exact value and radiance where the expression is the inverse sign of negative squared of three divided by two. Now the answer two provided are a negative pi divided by two B negative pi divided by three C negative pi divided by four and D negative pi divided by six. Now for a question like this, let's give ourselves an if and then situation. So if the inverse sign of negative squared of three divided by two is equal to X, then the regular sign of X is equal to the negative squared of three divided by two. And that's how we can switch between inverse sign and regular sign. Now we can recall from the unit circle and it's very important to be able to recall values from the unit circle right away. So from the unit circle, we know that sign of pie divided by three is equal to the square, the positive squared of three divided by two, which means that therefore we want negative sign of pi divided by three. If because if, if positive sign of pi divided by three is equal to squared of three divided by two, then negative sign of pi divided by three will give us our answer of negative squared of three divided by two. So how do we get there? Well, let's note that negative sign of a theta is equal to a sign of negative theta. So negative sign of pi divided by three is equal to a sign of negative pi divided by three. And this will give us, as we said, our negative square root of three divided by two, which means that X is equal to negative pi divided by three. So we're left with inverse sign of negative square root of three divided by two is equal to negative pi divided by three. And that will be the answer for this question which matches with answer choice B and we can see how important it is to be able to know about the unit circle and be able to recall different values. For example, in this case, that exact value wasn't the answer, but we were able to go from that exact value and do a small change to get to our final answer. So I hope that was helpful. And until next time.

Find the exact value of each expression. sin⁻¹ √2/2

Key Concepts

Inverse Sine Function (sin⁻¹ or arcsin)

Exact Values of Sine for Special Angles

Domain and Range Restrictions of Inverse Trigonometric Functions

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